Upper Bounds of AZI and ABC Index for Transformed Families of Graphs

Topological index is a mapping which corresponds underlying graph with a numeric value and invariant up to all the isomorphisms of graph. Our study is based on a partial open question regarding topological indices: for which members of n-vertex graph family, certain index has minimum or maximum value? In this work, we answered the above-mentioned question regarding AZI and ABC for transformed families of graphs Γ n k , l and A α Γ n k , l . We investigated the fact of pendent paths and the transformation A α over these indices and developed the tight upper bounds regarding these families of graphs. Moreover, we characterized transformed graphs associated with maximum values of these indices.